The oscillation characteristics of a 40 GHz, 1-3 ps regeneratively and harmonically mode-locked erbium-doped fiber laser have been investigated in detail with respect to stability, linewidth, and mode hopping. We show that because the Q value of the microwave filter in the feedback loop is limited to around 1000, which is almost the same as that in a 10 GHz laser, the cavity length should not be greatly increased as this would result in as much as a fourfold increase in the number of longitudinal beat signals. We undertook a detailed stability analysis by using three cavity lengths, 60, 80, and 230 m. The 80 m long cavity greatly improved the long-term stability of the laser because the supermode noise was suppressed and there were not too many longitudinal modes. We measured the linewidth of the longitudinal mode of the laser using a heterodyne method, and it was less than 1 kHz. We also point out that there is a longitudinal mode hopping effect with time that is induced by very small changes in temperature.